# How do you convert r = -2 csc Ө into cartesian form?

Jul 22, 2016

$y = - 2$

#### Explanation:

For this problem it's good to know some trigonometric identities. For example.

Remember that in polar coordinates, we write

$x = r \cos \left(\theta\right)$, $y = r \sin \left(\theta\right)$, and ${r}^{2} = {x}^{2} + {y}^{2}$

Since we know that $\csc \left(\theta\right) = \frac{1}{\sin} \left(\theta\right)$, we can try to rewrite our polar equation.

$r = - 2 \csc \left(\theta\right) \to r = - 2 \cdot \frac{1}{\sin} \left(\theta\right)$

If we multiply both sides by $\sin \left(\theta\right)$, we can simply replace it with $y$:

$r = - 2 \cdot \frac{1}{\sin} \left(\theta\right)$

$r \sin \left(\theta\right) = - 2$

Thus, in cartesian form, we get

$y = - 2$